# 1. Logic gates can be used to replace switches. Logic gates are easier to work with than switches, and it is easy to design and implement logic circuits in terms of gates. Consider the following problem: A system uses 3 switches A, B and C; a combination of switches determines whether an alarm, X, sounds. If switch A or switch B are in the ON position and if switch C is in the OFF position then a signal to sound an alarm, X, is produced. Design the logic of the circuit. Draw the circuit. Use the appropriate logic gates. 2. Consider three different processors P1, P2, and P3, executing the same instruction set. P1 has a 2 GHz clock rate and a CPI of 1.5. P2 has 2.0 GHz clock rate and a CPI of 1.0. P3 has a 4 GHz clock rate and a CPI of 2.5. Which processor has the highest performance? Please be sure to show and explain the detailed steps of how you arrived at your answer in your submission. Compose your work using a word processor (or other software as appropriate). Be sure to check your work and correct any spelling or grammatical errors before you upload it.

1. Solution:

To design the logic circuit for the given problem, we need to consider the conditions mentioned. The alarm, X, will sound if either switch A or switch B is ON and switch C is OFF. This can be represented using logic gates.

First, let’s define the inputs and outputs:

Inputs:

– Switch A (A)

– Switch B (B)

– Switch C (C)

Output:

– Alarm (X)

Now, let’s break down the conditions:

– If switch A or switch B is ON, we can represent this using the OR gate.

– If switch C is OFF, we can represent this as the complement of switch C using the NOT gate.

Based on the conditions and logic gates mentioned above, the logic circuit can be designed as follows:

________

A -| |

| OR -|

B -|________| AND —- X

________

C -| NOT |

|________|

In this circuit, the inputs A, B, and C are connected to the OR gate and the NOT gate. The output of the OR gate and the complement of C are connected to the AND gate, which produces the output X.

This logic circuit will produce an output signal X (the alarm) whenever switch A or switch B is ON and switch C is OFF.

2. Solution:

To determine which processor has the highest performance, we need to consider the clock rate and CPI (Clock Cycles Per Instruction) of each processor.

The performance of a processor can be quantified using the following formula:

Performance = Clock Rate (GHz) * CPI

Let’s calculate the performance for each processor:

Processor P1:

Clock Rate = 2 GHz

CPI = 1.5

Performance P1 = 2 GHz * 1.5 = 3

Processor P2:

Clock Rate = 2 GHz

CPI = 1.0

Performance P2 = 2 GHz * 1.0 = 2

Processor P3:

Clock Rate = 4 GHz

CPI = 2.5

Performance P3 = 4 GHz * 2.5 = 10

Comparing the performances of the three processors, we can see that Processor P3 has the highest performance with a value of 10. Therefore, Processor P3 is the most efficient among P1, P2, and P3.

In conclusion, the processor with the highest performance is Processor P3, with a clock rate of 4 GHz and a CPI of 2.5.

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